A classic example of a subsystem code is the Bacon-Shor code [1]}
having physical qubits on the vertices of an \(L\times L\)  lattice (so \(n = L^2\) ).
The gauge group is generated by neighboring pairs of \(XX\)  and \(ZZ\)  operators across the
horizontal and vertical links respectively. The logical quantum information is encoded by a
string of \(X\)  operators along a horizontal line and a string of \(Z\)  operators along a vertical
line, and the code distance is \(L = \sqrt{n}\) .
